Robust mobile digital communication is difficult to accomplish because of the deleterious effects of the environment on the propagation characteristics of the radio-frequency (RF) channel (from about 0 to 100 Gigahertz). Atmospheric conditions and variations in terrain, foliage, and the distribution and density of man-made structures and operating machinery strongly affect the characteristics of the medium which RF signals traverse. Satellite communication systems are typically limited by insufficient electromagnetic radio-frequency (RF) field strength due to the presence of background cosmic, atmospheric, and man-made noise which together establish an irreducible noise floor. Satellite systems may also be limited by the thermal noise of the active electronic components used in the implementation of the receiver system. Terrestrial mobile communications systems are also subject to performance degradation due to the effects of background and thermal noise. However, terrestrial mobile receiver systems are further degraded by multipath propagation due to the reception of signals corresponding to paths other than the line-of-sight (LOS) propagation path.
A method which is used to combat the deleterious effects of multipath propagation, as well as interference from other sources, is "spread spectrum" modulation [reference: R. L. Pickholtz, D. L. Schilling, and L. B. Milstein, "Theory of spread-spectrum communications--a tutorial, IEEE Transactions on Communications, Vol. 30, No. 5, pp. 855-884, May 1982]. See also U.S. Pat. Nos. 5,063,560; 5,081,543; 5,235,614; and 5,081,645. In a spread spectrum communication system, the bandwidth occupied by the digital data message is expanded (spread) in the transmitter by multiplying the data message by a spreading signal or sequence which is unrelated to the data message. The spreading effect is collapsed in the receiver by the process of correlation. Multipath and other forms of interference which are frequency-selective then only perturb part of the spread signal. However, spread spectrum methods are no more effective than narrowband modulation methods, for example, the method of Orthogonal Frequency Division Multiplexing (OFDM) [reference: W. Y. Zou and Y. Wu, "COFM: an overview," IEEE Transactions on Broadcasting, Vol. 41, No. 1, pp. 1-8, March 1995], in combating the effects of wideband noise.
A disadvantage of spread spectrum modulation is that it typically has relatively poor spectrum efficiency (i.e. less than one bit per Hertz per information symbol). The ability of the spread signal to combat narrowband forms of interference is determined by the "processing gain" of the spread spectrum system, which is essentially the ratio of the spread signal bandwidth to that of the original data message. Therefore, in order to ensure sufficient processing gain, the data message bandwidth is a small fraction of the spread signal bandwidth (e.g. less than about one-tenth). As a result, it may be difficult to use single-carrier spread spectrum modulation in circumstances where the available bandwidth is strictly limited and the necessary data throughput requires high spectrum efficiency.
A spread spectrum communication system requires the use of at least one transmitted spreading signal. It is possible to increase the throughput of a spread spectrum communication system through the consideration of additional spreading signals in the determination of the transmitted signal. Two prior art methods for increasing the information efficiency of a spread spectrum communication system are "m-ary orthogonal" modulation and "m-ary biorthogonal" modulation [reference: W. C. Lindsey and M. K. Simon, Telecommunication Systems Engineering. Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1973, p. 198, pp. 210-225]. Both of these methods differ from methods of simultaneously multiplexing spreading signals, in which a plurality of spread signals are simultaneously transmitted in a single information symbol or baud. In m-ary orthogonal modulation, only one signal selected from a plurality of spreading signals is transmitted for the duration of the baud. If there are a number, denoted M, of signals in the signal set, then with m-ary orthogonal modulation, each information baud conveys log.sub.2 M information bits because the determination as to which one of the M signals (i.e. a 1-of-M choice) can be represented with log.sub.2 M decision bits, hereafter known as the "selection" bits.
Prior art m-ary biorthogonal modulation is similar to m-ary orthogonal modulation except that the polarity of the transmitted signal is also modulated by some bits in the data message. While the m-ary orthogonal system conveys log.sub.2 M information bits in a baud through the selection of the transmitted signal, the m-ary biorthogonal system conveys (log.sub.2 M)+1 information bits through the selection of the transmitted signal (log.sub.2 M bits as before) and determination of the transmitted signal polarity by one bit per information symbol, hereafter known as the "polarity bit". The specific prior art embodiment of biorthogonal modulation where M is one (1) corresponds to zero (0) selection bits and only one polarity bit. This is equivalent to prior art "antipodal" (also known as bipolar, biphase, BPSK) modulation where the signal is always transmitted and only the polarity of said signal is modulated. The embodiment with M equal to one (1) of biorthogonal modulation is a degenerate example and is not considered further. In the instant application, the minimum valid number M of signals for m-ary orthogonal or m-ary biorthogonal modulation is two (2). Furthermore, only binary powers of two are considered for values of M (i.e. two, four, eight, sixteen, and so forth). The methods of m-ary orthogonal and m-ary biorthogonal modulation are unrelated to the modulation method of "m-ary amplitude" modulation, where one of a plurality of amplitude scale factors are applied to a spread signal in order to increase the information density.
In order to implement a receiver for transmitted m-ary orthogonal or biorthogonal signals, the signals in the signal set are identically embodied in both the transmitter and the receiver system and are pairwise distinct for all M signals. Furthermore, the signals must all be pairwise orthogonal or approximately orthogonal (AO). Mutually orthogonal or orthogonal signals are defined as having a crosscorrelation value (sum) of about zero, when properly synchronized. The crosscorrelation value of two signals is proportional to the sum or equivalently the integration of the pairwise product of the two signals (i.e. the inner product). AO signals are distinguished from orthogonal signals by having the characteristic of a small-magnitude crosscorrelation value, which is non-zero. Either orthogonal or AO signals may be used with either m-ary orthogonal or m-ary biorthogonal modulation. As the value of M is increased, the maximum permitted crosscorrelation value among signal pairs for proper operation of the receiver system is decreased. Whereas perfectly orthogonal signals do not interfere with one another in a correlation receiver, when AO signals are implemented, error correcting codes are typically required in order to reduce the irreducible error level (known as the code noise or self-noise) due to mutual crosscorrelation interference between the non-orthogonal AO signals.
Spreading signals can be determined by various methods. Some spreading signals or sequences which have been implemented in prior art spread spectrum systems include, but are not limited to, distinct m-sequences, which are also known as pseudonoise (PN) sequences or maximal-length sequences [reference: D. V. Sarwate and M. B. Pursley, "Crosscorrelation properties of pseudorandom sequences," Proceedings of the IEEE, Vol. 68, No. 5, pp. 593-619, May 1980], distinct phases of a single m-sequence [reference: S. L. Miller, "An efficient channel coding scheme for direct sequence CDMA systems," Proceedings of MILCOM '91, pp. 1249-1253, 1991], orthogonal m-sequences with bit stuffing as disclosed by Gutleber in U.S. Pat. No. 4,460,992, issued Jul. 17, 1984, Gold codes, Kasami codes, Hadamard codes, and Bent codes [reference: S. Tachikawa, "Recent spreading codes for spread spectrum communications systems," (translated) Electronics and Communications in Japan, Part 1, Vol. 75, No. 6, pp. 41-49, June 1992]. It is also possible to determine spreading sequences which occupy the available bandwidth and which are orthogonal using matrix eigenvector methods, such as disclosed in U.S. Pat. No. 4,403,331 by P. H. Halpern and P. E. Mallory, or by using orthonormal wavelets as disclosed by Resnikoff, et al. in U.S. Pat. No. 5,081,645. Some of the previously disclosed methods use orthogonal or approximately orthogonal spread spectrum signals together with antipodal data modulation in a simultaneously multiplexed system. The orthogonal spreading sequences determined for such methods (sometimes referred to as "multiple access" methods) may also be suitable for m-ary orthogonal or m-ary biorthogonal modulation, where only one of a plurality of signals is transmitted (i.e. non-multiplexed). The above-listed spreading sequences or signals may be used in this invention, as discussed hereinafter.
Error correction digital codes (ECC) are an important method of combating the effects of noise, outside interference, and self-noise in spread spectrum communication systems, regardless of the modulation method. An ECC method consists of a system (i.e. an algorithm and its implementation) of encoding an original data message through the incorporation of redundancy information together with a system for decoding the encoded message so as to recover the original message. The bit rate throughput required to represent the encoded message is larger than that of the message itself. The average ratio of the original message length to the encoded message length is known as the "code rate". As the amount of redundancy is increased, the code rate decreases, which diminishes the decoded message throughput of the system. However, the probability of error in determining the message at the receiver, after ECC decoding, is typically diminished by a much greater amount, so that the loss of some throughput in order to dramatically improve the reliability of the communication system is acceptable. A measure of the improvement is the "coding gain" of the ECC. The coding gain may be interpreted as the effective increase in the signal-to-noise ratio (SNR) brought about by the use of the ECC in a equivalent system without ECC or with reference to some other ECC method. ECC methods in which the amount of ECC applied to message bits is approximately equal for all bits are known as equal error protection (EEP) ECC methods. ECC methods in which the amount of ECC redundancy varies according to the function or purpose of the bit are known as unequal error protection (UEP) ECC methods. UEP ECC methods are typically used when the relative importance of the transmitted bits varies considerably. The conditions for continuous mobile reception may be so difficult that practical code rates are usually about one-half or less, which is equivalent to one hundred (100) percent redundancy.
A block diagram of a prior art receiver system for a biorthogonally modulated signal is shown in FIG. 1. The received RF signal is first amplified and filtered with a bandpass filter in tuner 1 to remove interference and noise which is outside of the bandwidth of the spread spectrum signal. The RF signal is typically frequency-translated to a lower frequency, known as the intermediate frequency (IF), for further processing, which simplifies the implementation. In some digital systems, the IF frequency is zero, which requires that the remaining processes be implemented with complex digital arithmetic (i.e. real and imaginary components). The tuner also accomplishes the function of automatic gain control (AGC) so that the received signal energy is made to be approximately constant for subsequent processing. The combined RF functions are abbreviated as RF tuner 1.
In many conventional FIG. 1 systems, the signal is converted (quantized) from an analog representation (i.e. voltage or current) to a digital representation by analog-to-digital converter (ADC) 3. The number of bits in the implementation of the ADC is chosen to preserve sufficient dynamic range in the digitized signal so that the irreducible error level caused by ADC quantization noise does not significantly degrade the receiver system performance. Typically, the number of bits is between six (6) and twelve (12), inclusive. The received and quantized signal is made synchronous with the transmitter in baud frequency and carrier frequency by baud clock recovery 5 and carrier frequency recovery 7 subsystems. Typically, these functional blocks are implemented with early/late or pulse-swallowing algorithms, phase-lock loops (PLLs) and voltage-controlled oscillators (VCOs), and/or frequency-lock loops (FLLs). The overall function of recoveries 5 and 7 is to eliminate frequency offsets caused by variation in components and the effect of Doppler frequency shift. The synchronization also establishes the proper timing (i.e. phase relationship) so that the magnitude of the crosscorrelation values between the possible signals in the biorthogonal signal set are at a minimum at an instance in the baud interval known as the "sampling point".
The digitized and synchronized signal is optionally equalized by adaptive equalizer 9 in order to partially correct for the effects of RF signal dispersion caused by the frequency-selective characteristics of the RF propagation channel. The equalizer also mitigates phase and amplitude errors caused by implementation loss due to analog components in the transmitter and receiver systems. Equalizer 9 may be implemented with a finite-impulse response (FIR) transversal filter or an infinite-impulse response (IIR) recursive filter or a combination thereof. The coefficients of the equalization filter are determined by a tap-weight update algorithm and are updated at a rate sufficient to reasonably track changes in the RF propagation characteristics. Some prior art methods for equalization include, but are not limited to, minimum mean square estimation (MMSE), least mean square (LMS), and recursive least square (RLS) algorithms, all of which are known.
The equalized signal is propagated to biorthogonal demodulator 11. The function of biorthogonal demodulator 11 is to determine estimates of the log.sub.2 M encoded selection bits and one encoded polarity bit in each information baud. The biorthogonal transmitter system (not shown) transmits one of the plurality of M signals from the biorthogonal signal set in each baud. The bit representation of the index of the biorthogonal signal (i.e. 1-of-M choice) is represented by the encoded selection bits. The polarity of the resulting signal is modulated in the transmitter system by multiplying the determined signal by a factor of positive unity (one) or negative unity, arbitrarily corresponding to an encoded polarity bit value of zero or one, respectively. After demodulation, the estimated section and polarity bits are organized as a serial bit sequence and processed by deinterleaver 13. The function of deinterleaver 13 is to reverse the effect of the shuffling process of the corresponding interleaver, if present, in the transmitter system (not shown). Interleaving is a method of time-diversity in which groups consisting of one or a plurality of bits are re-arranged by way of a shuffling algorithm which is a bijection. The incorporation of an interleaver in the transmitter system and consequently a deinterleaver in the receiver system is optional, but they are frequently used in mobile communication systems to combat burst errors. The deinterleaved sequence of bits is substantially similar to that after ECC encoding in the transmitter system, except for the occurrence of errors.
After deinterleaving 13, the selection and polarity bit estimates are decoded by error correction code decoder 15 in order to recover the original data message. The ECC decoder reverses the effects of the ECC encoder (not shown) in the transmitter system according to the error correction code, substantially reducing the number of bit errors after decoding. The size of the decoded message is made smaller than the message prior to decoding by an amount corresponding to the code rate factor.
The system of ECC decoder 15 implements an algorithm which is essentially the reverse of the ECC encoder in the transmitter (not shown). In the transmitter system, ECC encoding is performed after bit scrambling and prior to interleaving and biorthogonal modulation. The optimum ECC decoder is related to the optimum ECC encoder. The optimum encoder for a specific communication system depends on the expected characteristics of the error distribution at the receiver, which requires knowledge of the specific modulation method and the expected RF channel impairment. Typically, convolutional codes or block codes, or a combination thereof, are implemented in the encoder in the transmitter and corresponding ECC decoder in the receiver. Convolutional codes with soft-decision Viterbi decoding in the receiver have been found to be optimum in circumstances where the error distribution is substantially random, uncorrelated, and resembles a Gaussian function. However, in bursty environments, block codes may be preferable (e.g. binary BCH codes, Reed-Solomom codes, concatenated parity-Reed-Solomon codes, and/or quadratic residue codes). In the ECC encoder in the transmitter (not shown), the length of the scrambled source message is increased by a factor which is the reciprocal of the code rate.
After ECC decoding 15, the decoded message is propagated to descrambler 17. Scrambling in the transmitter and consequently descrambling 17 in the receiver is optional. Scrambling is typically used to eliminate long runs of consecutive binary ones and zeroes and to cause approximately equal probabilities for the occurrence of the binary digits zero and one in the transmitted source message. Scrambling may be accomplished in the transmitter by multiplying the source message bit sequence by a binary polynomial, for example a PN-sequence, using binary arithmetic. Similarly, in order to descramble the decoded bit sequence message, the decoded and synchronized bit sequence is multiplied by the same binary polynomial. The distribution of the sequence generated by the binary scrambling polynomial is approximately uniform and has a very long period. After descrambling 17, the estimated message 19 substantially resembles the source data message that was transmitted, except for the occurrence of errors.
FIG. 2 is a block diagram of the prior art biorthogonal demodulator 11 in FIG. 1 where M is two (2). The equalized signal 21 is applied to a plurality of correlators 23 and 25. Each correlator determines the inner product between the input signal 21 and a spreading signal, when properly synchronized about the sampling point. Correlators are typically implemented with integrators and sample-hold circuits in analog embodiments and multiply-accumulate (MAC) circuits in digital embodiments. The dynamic range (analog embodiment) or bit width (digital embodiment) is determined so that the irreducible error level due to the implementation does not significantly degrade the receiver performance. The spreading signals which are input to the correlators 23 and 25 are generated by signal generators 27 and 29, respectively, resulting in correlation sums 31 and 33. In general, for a biorthogonal signal set with M orthogonal or AO signals, M correlators and M signal generators are required in the receiver in order to generate M correlation sums. The signal generators are identical to those in the corresponding transmitter system where the result of only one of the signal generators is transmitted, together with polarity modulation, in each baud. For the specific embodiment where M=2, the received signal corresponds to one of two possible transmitted orthogonal or AO signals in each baud, together with polarity modulation. The correlation sums 31 and 33 are propagated to the absolute-value functions 35 and 37, respectively, which remove the polarity information from the correlation sums by discarding sign-bit information. The correlation sums are also propagated to limiters 39 and 41. The limiters (also known as 1-bit quantizer or hard-limiters) operate in a manner opposite to that of the absolute-value functions. While the absolute-value functions remove polarity information and preserve magnitude information in order to determine the selection bits, the limiters remove magnitude information and preserve only polarity information in order to determine the polarity bits.
The correlation sum magnitudes are compared by the comparison operator 43 in order to determine which of the two correlation sum magnitudes is the largest. The signal in the biorthogonal signal set corresponding to the largest correlation sum magnitude is determined to be the signal which is most likely to have been transmitted in the baud interval. The comparison operation is typically implemented with a comparator circuit. The comparator results in a binary digit which corresponds to the index of the signal which was estimated to have been transmitted. For example, in the biorthogonal transmitter system, if an encoded selection bit value of one results in the transmission of the signal corresponding to signal generator 27 in the receiver, then the comparator 43 is implemented so that it results in the binary digit one when the magnitude of the correlation sum 31 is greater than the magnitude of the correlation sum 33. Correspondingly, if an encoded selection bit value of zero in the transmitter results in the transmission of the signal corresponding to signal generator 29 in the receiver, then the comparator 43 is implemented so that it results in the binary digit zero when the magnitude of the correlation sum 33 is greater than the magnitude of the correlation sum 31. If the result of the comparison operator is ambiguous (i.e. equal correlation sum magnitudes), then the value of the comparison operator is determined randomly. The result 45 of the comparison operator 43 is the selection bit estimate.
The selection bit estimate is the control input for polarity bit multiplexor 47. Multiplexor 47 propagates only one of the plurality of limiter values, which are the multiplexor data inputs, according to the selection bit. For all representations of a multiplexor in the block diagrams in this disclosure, the control input is distinguished from the data inputs by the label "S". For polarity bit multiplexor 47, the control bits are the selection bits. Multiplexor 47 is implemented so that the limiter value corresponding to the correlation sum magnitude with the largest value is propagated. In the previous example, multiplexor 47 propagates the result of limiter 39 if the result of comparison operator 43 is binary value one. Multiplexor 47 propagates the result of limiter 41 if the result of comparison operator 43 is binary value zero. The result 49 of the multiplexor is the polarity bit estimate. The selection bit 45 and polarity bit estimates 49 are together propagated beyond biorthogonal demodulator 11 to deinterleaver 13 shown in FIG. 1.
In the general case where M is greater than two, comparison operator 43 is replaced with a "maximum-value" function. The maximum-value function results in the index value of the signal whose correlation sum magnitude is the largest. The index value is represented by log.sub.2 M selection bits (i.e. a 1-of-M choice). Index values are organized so that the bit sequences in the transmitter and those recovered by the receiver system are identical in the absence of demodulation errors (i.e. for a particular index, the same signal is selected in the biorthogonal modulator as is determined in the biorthogonal demodulator). In general, there are a plurality of M signal generators, M correlators, and M absolute-value functions in the biorthogonal demodulator for a biorthogonal signal set with M possible orthogonal or AO signals. In general, polarity multiplexor 47 selects from one of M inputs according to log.sub.2 M estimated selection bits. The polarity of the correlation sum with the largest magnitude is propagated as the demodulated polarity bit. The result of the demodulation of a single information baud is a sequence of (log.sub.2 M)+1 bits.
A disadvantage of the prior art biorthogonal demodulator in FIG. 2 is that soft-decision reliability information for the selection bit estimate, beyond the minimum log.sub.2 M selection bits which represent the signal choice, is not useful in the determination of which polarity bit estimate is selected by the polarity bit multiplexor 47. The selection and polarity bit estimates are both determined in the prior art biorthogonal demodulator 11, while improvements due to soft-decision reliability information are typically not produced until after ECC decoding 15. Thus, even if the selection bit error rate is eventually reduced by ECC decoding, the selection bit error rate prior to ECC decoding, in the biorthogonal demodulator 11, may be high (e.g. 1.times.10.sup.-3 to 1.times.10.sup.-2), which results in a degradation in the polarity bit error rate performance.
The probability of error in determining the selection bit in prior art FIGS. 1-2, P.sup.S.sub.b, prior to error decoding, for the specific embodiment where M=2 and the RF channel impairment is additive white Gaussian noise is known to be [reference: G. R. Cooper and C. D. McGillem, Modern Communications and Spread Spectrum. New York: McGraw-Hill, Inc., 1986, pp. 233-234]: ##EQU1## where E.sub.S is the energy in any one of the signals in the biorthogonal signal set, which are assumed to be equiprobable and equal in energy, N.sub.b0 is the noise spectral density, and Q is the complementary cumulative distribution function for the Gaussian probability density function (a.k.a. the Marcum Q function) [reference: G. R. Cooper, et al., ibid., pp. 423-425]. The noise spectral density is determined by measuring only the noise power through the bandwidth of the received signal. In the general case where M is greater than two, the error event probability for the selection bits considered together as the selection word, P.sup.S, is given only approximately by the union bound: ##EQU2## For the specific embodiment where M=2, the selection word error rate and the selection bit error rate are equal. However, in general, for M greater than two, the selection word error event probability, P.sup.S, and the selection bit error probability, P.sup.S.sub.b, are related but unequal. In some literature references to biorthogonal modulation (e.g. G. R. Cooper, et al., ibid. pp. 233-234), the term "N" or "M" refers to the total size of the signal set, including the orthogonal or AO signals with both positive and negative polarities. In this disclosure, the term "M" refers only to the number of distinct orthogonal signals (i.e. the dimension of signal set and N=2M) since the polarity of the signal is determined by the modulation and not the signal design.
An exemplary distribution of the correlation sum values determined in the prior art biorthogonal demodulator 11 is shown in FIG. 3 with one of two possible orthogonal signals transmitted in the presence of additive white Gaussian noise. Since the signals are assumed to be equiprobable, it is sufficient to consider the possible correlation sums in the event of the transmission of only one of the signals for all baud intervals and with a fixed arbitrarily positive polarity. The abscissa values are normalized by a factor equal to the signal energy, E.sub.S in Equation (1). In the absence of noise, there would be two point masses, centered at zero (0) and positive one (+1), respectively. The presence of noise smears the point masses out into continuous distributions. Distribution region 51 illustrates the correlation between the received signal and the orthogonal signal which corresponds to the correct selection bit. Distribution region 53 represents the correlation between the received signal and the other orthogonal signal (i.e. corresponding to the incorrect determination of the selection bit). The mean abscissa value of region 53 is about zero because the two signals in the biorthogonal signal set are presumed to be orthogonal. Since the detection method for biorthogonal modulation is a comparison of correlation sum magnitudes, errors occur in overlapping region 55.
However, biorthogonal system errors also occur in regions 57 and 59 which correspond to the images of the overlapping region 55 for the opposite polarity. These additional error events are caused because the correlation sum polarity information cannot be used to determine which of the two signals was most likely to have been sent. Instead, the polarity of the correlation sum is used to determine the remaining information bit, the polarity bit. The mean abscissa values of regions 51 and 53 are separated by Euclidean distance 61 which is a distance equivalent to the signal energy when the normalization is taken into consideration.
The probability of error in determining the polarity bits in the biorthogonal receiver system of prior art FIGS. 1-2 is more complicated and depends upon the probability of error for the selection bits. FIG. 5 is a graph which illustrates an exemplary distribution of the correlation sums in the determination of the polarity bits for the biorthogonal receiver when the impairment is AWGN and the selection bit is correctly demodulated. The abscissa values are normalized as in prior art FIG. 3. Region 63 corresponds to the distribution for a positive polarity modulation (arbitrarily, binary value zero) of the transmitted signal and region 65 corresponds to the distribution for a negative polarity modulation (arbitrarily, binary value one) of the transmitted signal. If the selection bit is correctly identified, which occurs with probability (1-P.sup.S.sub.b), the conditional polarity bit error probability, P.sup.P.vertline.S.sub.b, is: ##EQU3## The Marcum Q function decreases monotonically as its argument is increased. Since the numerator of the radical in Equation (3) is twice that in Equation (1), the conditional error probability in determining the polarity bits is significantly smaller than that of the selection bits in Equation (1), if the selection bit is correctly identified. The argument of the Q function is typically considered as a measure of the receiver signal-to-noise ratio (SNR). The conditional polarity bit error probability given by Equation (3) has more than a three decibel advantage (i.e. factor of two in SNR), when compared to the selection bit error probability given by Equation (1). A precise determination of the SNR advantage requires inversion of Equation (1), which has no closed-form solution and can only be determined numerically. The improvement in SNR is evident by the larger Euclidean distance 67 between the possible distribution regions 63 and 65 shown in FIG. 4.
However, when the selection bits are incorrectly identified in the biorthogonal demodulator, which happens with probability P.sup.s.sub.b the conditional probability of error for the polarity bits is one-half (1/2) because the polarity of the correlation sum corresponding to the incorrect biorthogonal signal is unrelated to the correlation sum of the correct signal. The polarity determination is then essentially random; in other words, a coin toss. The overall error probability for the polarity bits, P.sup.P.sub.b, is the weighted sum of the two polarity bit conditional error probabilities: ##EQU4##
By inspection of Equation (4), even when the conditional probability of error in the determination of the polarity bits is zero, which would require an infinite SNR, the polarity bit error is still non-zero and is substantially determined by the probability of error of the selection bits, P.sup.S.sub.b. Thus, the benefit of the SNR advantage in the conditional polarity bit error rate determination shown in Equation (3) is diminished by the selection bit error rate of Equation (1), which is typically substantially worse. This is a disadvantage to the prior art method of m-ary biorthogonal demodulation when compared to simultaneously multiplexed modulation and demodulation methods such as OFDM.
The prior art biorthogonal receiver system has been previously described and shown in FIGS. 1-2. U.S. Pat. No. 4,247,943 to Malm discloses the use of orthogonal or biorthogonal codewords in a receiver system for a signal that is generated by frequency-shift keying together with local phase-shift-keying. The receiver makes use of crosscorrelation sums determined between the received signal and four orthogonal signals, corresponding to the in-phase and quadrature component at two frequencies, to demodulate the signal.
Biorthogonal codewords [reference: W. C. Lindsey and M. K. Simon, Telecommunications Systems Engineering, ibid., pp. 188-194] are sets of binary sequences (i.e. ones and zeroes) which are constructed so that the permissible codewords are either pairwise orthogonal or complementary to each other. Biorthogonal codes are typically used to phase-modulate a narrowband sinusoidal signal. Methods for demodulating a biorthogonal signal set and decoding a biorthogonal codeword are unrelated except superficially in that both methods require magnitude comparisons among a plurality of possible signals or codewords.
U.S. Pat. No. 4,730,344 to Saha discloses a four dimensional modulation method known as Quadrature--Quadrature Phase-Shift Keying (QQPSK). The system of the '344 patent makes use of the in-phase and quadrature components of a signal with further data shaping of each component according to two orthogonal pulse shapes. This is equivalent to simultaneous multiplexing of antipodal-modulated orthogonal signals and not biorthogonally modulated signals. The reception of antipodal signals is unrelated to biorthogonal demodulation and the receiver of the instant invention.
U.S. Pat. No. 4,700,363 to Tomlinson et al discloses a method of m-ary phase modulation and unequal error protection. The system of '363 uses m-ary phase-shift keying together with the possible use of biorthogonal binary phase codewords. In general, m-ary phase modulation is different from m-ary biorthogonal modulation because the possible phase states in m-ary phase modulation are not pairwise orthogonal or approximately orthogonal. Hence, m-ary phase modulation is unrelated to the instant invention.
Accordingly, it is apparent from the above that there exists a need in the receiving art for: (i) limiting or diminishing the coupling between the selection and polarity bit error probabilities; (ii) preserving selection bit soft-decision reliability information for use in the determination of the polarity bits; (iii) reducing the polarity bit error rate; and (iv) reducing the overall bit error rate in biorthogonal demodulation.